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The directional coupler is a fundamental element of wave-based circuits. The state of the art for the spin-wave directional couplers consists mostly of macroscopic waveguides or two-dimensional planar systems. In this Letter, we present the design of the nanoscale spin-wave vertical directional coupler with a very high efficiency exceeding 99.5%. We demonstrate that the operation of the coupler can be controlled by the magnitude of the external magnetic field. Moreover, it can perform multiplexing and demultiplexing of the spin-wave signal. Such a device ought to become an essential element of the three-dimensional magnonic circuits., Comment: Main part: 6 pages, 5 figures. Supplementary: 2 pages, 2 figures

Artificial spin-ice systems, consisting of arrays of interacting ferromagnetic nanoelements, offer a versatile platform for reconfigurable magnonics with potential in GHz logic and neuromorphic computing. However, weak dipolar coupling between nanoelements severely limits their functionality. We numerically demonstrate a rich spin-wave spectrum in a square spin-ice structure immersed in a perpendicularly magnetized ferromagnetic matrix, which is different from a single spin-ice system. We observe a strong magnon-magnon coupling between the bulk second-order mode of the nanoelements and the fundamental mode of the matrix, supported by a pronounced anticrossing frequency gap. We show that, in addition to the dipolar coupling, exchange interactions at the nanoelement-matrix interface play a crucial role in this hybridization. Furthermore, the strength of the coupling can be enhanced by almost 40% just by reconfiguring the magnetization at the vertices from low-energy to high-energy monopole states. These results open the way to exploit artificial spin-ice systems for magnonic applications, taking advantage of the strong coupling and vertex-dependent dynamics.

This study investigates the nucleation, dynamics, and stationary configurations of Abrikosov vortices in hybrid superconductor-ferromagnetic nanostructures exposed to inhomogeneous magnetic fields generated by a ferromagnetic nanodot. Using time-dependent Ginzburg-Landau simulations and Maxwell's equations, we observe and provide an explanation for the evolution of curved vortex structures that undergo creep-like deformation while reaching a steady state. Spatial variations in the Lorentz force, along with the interaction between geometric constraints and vortex interactions, give rise to unusual stationary vortex configurations that gradually change with increasing field strength, a behavior not seen in homogeneous magnetic fields. These findings reveal complex pinning mechanisms, providing valuable insights for the optimization and further advancement of nanoscale superconducting systems.

Results of extensive combined experimental and theoretical investigations on static and dynamic properties of Ir/Co/Pt multilayer with low uniaxial anisotropy and asymmetric Ir/Co and Co/Pt interfaces responsible for large interfacial Dzyaloshinskii-Moriya interaction (IDMI) are presented. Within longitudinal magneto-optical Kerr effect-based microscopy and magnetic force microscopy studies a complex magnetic configuration was detected: large in-plane magnetized domains of several dozen micrometers size were modulated by a weak stripe domain pattern with periods of about 100 nm. Using Brillouin Light Scattering spectrometry, the hysteresis of the Stokes and anti-Stokes peaks frequencies was observed as a function of the magnetic field. This hysteretic behavior associated with IDMI-induced asymmetry of spin waves dispersion is correlated with switching of the large macro-domains. Using micromagnetic simulations we determine field-dependent magnetization distributions and dispersion relations, proposing an explanation of the observed behavior. The investigated nanostructure can be used as non-volatile spin waves velocity switcher., Comment: Accepted for publication in Physical Rewiev B, https://journals.aps.org/prb/accepted/ce071O5bHbf17c5401c04140b8bb51c940576e842

We show, by means of micromagnetic simulations, inelastic scattering of spin-wave beams on edge-localized spin waves modes. The outcome of the investigated inelastic scattering is creation of new spin-waves beams of frequencies shifted by the edge mode frequencies. We report that inelastically scattered spin-wave beams in both stimulated splitting and confluence processes not only change their direction of propagation, but also undergo lateral shifts along the interface, analogous to the Goos-H\"anchen effect. We report that the lateral shifts of inelastically scattered beams can be much larger than the classical Goos-H\"anchen shifts for reflected spin waves, taking both positive and negative values. In addition, we report the cascade nonlinear excitation of spin-wave leaky modes accompanied by a substantial increase in the value of the lateral shift of the inelastically scattered spin-wave beam in the confluence process. Our results are an important contribution to the understanding of the nonlinear nature of spin waves, which is crucial for spin wave applications.

Extending the current understanding and use of magnonics beyond conventional planar systems, we demonstrate surface localization of spin-wave ferromagnetic resonance (FMR) modes by designing complex three-dimensional nanostructures. Using micromagnetic simulations, we systematically investigate woodpile-like scaffolds and gyroids - periodic chiral entities characterized by their triple junctions. The study highlights the critical role of demagnetizing fields and exchange energy in determining the FMR responses of 3D nanosystems, especially the strongly asymmetric distribution of the spin-wave mode over the system height. Importantly, the top-bottom dynamic switching of the surface mode localization across the structures in response to changes in magnetic field orientation provides a new method for controlling magnetization dynamics. The results demonstrate the critical role of the geometric features in dictating the dynamic magnetic behavior of three-dimensional nanostructures, paving the way for both experimental exploration and practical advances in 3D magnonics.

This research chapter provides a comprehensive overview of ferromagnetic gyroidal nanostructures, combining a review of state-of-the-art research with our new findings on their implications for 3D magnonics. Both static and dynamic magnetization studies show that non-trivial shape anisotropy, chirality, and inhomogeneous demagnetization fields influenced by specific crystallographic arrangements lead to multiple low-energy state magnetization textures, spin-wave mode localization, and controllable spin-wave propagation, highlighting the substantial potential of gyroidal nanostructures. The review integrates insights into micro/nano texturing to elucidate the intricate relationships between gyroidal geometry, chirality, and their effective magnetic properties, especially at microwave frequencies. Our study of resonance frequencies in gyroid samples under rotational field manipulation further reveals the significant influence of geometric anisotropy on ferromagnetic resonance signal strength. This chapter establishes a fundamental understanding of ferromagnetic gyroidal nanostructures, paving the way for their future investigation in 3D magnonics., Comment: 47 pages, 11 figures

Magnetic hopfions are localized magnetic solitons with a nonzero 3D topological charge (Hopf index). Herein, an analytical calculation of the magnetic hopfion gyrovector is presented and it is shown that it does not vanish even in an infinite sample. The calculation method is based on the concept of the emergent magnetic field. The particular case of the simplest nontrivial toroidal hopfion with the Hopf index $\|Q_H\|=1$ in the cylindrical magnetic dot is considered and dependencies of the gyrovector components on the dot sizes are calculated. Nonzero hopfion gyrovector is important in any description of the hopfion dynamics within the collective coordinate Thieles approach., Comment: 6 pages, 3 figures

Extending the scope of the self-imaging phenomenon, traditionally associated with linear optics, to the domain of magnonics, this study presents the experimental demonstration and numerical analysis of spin-wave (SW) self-imaging in an in-plane magnetized yttrium iron garnet film. We explore this phenomenon using a setup in which a plane SW passes through a diffraction grating, and the resulting interference pattern is detected using Brillouin light scattering. We have varied the frequencies of the source dynamic magnetic field to discern the influence of the anisotropic dispersion relation and the caustic effect on the analyzed phenomenon. We found that at low frequencies and diffraction fields, the caustics determine the interference pattern. However, at large distances from the grating, when the waves of high diffraction order and number of slits contribute to the interference pattern, the self-imaging phenomenon and Talbot-like patterns are formed. This methodological approach not only sheds light on the behavior of SW interference under different conditions but also enhances our understanding of the SW self-imaging process in both isotropic and anisotropic media.

We present a hybrid magnonic crystal composed of a chain of nanodots with strong perpendicular magnetic anisotropy and Dzyaloshinskii-Moriya interaction, positioned above a permalloy waveguide. The micromagnetic study examines two different magnetization states in the nanodots: a single-domain state and an egg-shaped skyrmion state. Due to the dipolar coupling between the dot and the waveguide, a strongly bound hybrid magnetization texture is formed in the system. Our results show complex spin-wave spectra, combining the effects of periodicity, magnetization texture, and hybridization of the propagating waves in the waveguide with the dot/skyrmion modes. The dynamics of the systems are characterized by several key features which include differences in band-gap sizes, the presence of flat bands in the skyrmion state that can form both bound and hybridized states, the latter sometimes leading to the presence of additional non-Bragg band gaps, and a broad frequency range of only waveguide-dominated modes in the single-domain state. Thus, the study shows that the proposed hybrid magnonic crystals have many distinct functionalities, highlighting their reconfigurable potential, magnon-magnon couplings, mode localization, and bound states overlapping with the propagating waves. This opens up potential applications in analog and quantum magnonics, spin-wave filtering, and the establishment of magnonic neural networks., Comment: 12 pages, 4 figures (18 pages, 8 figures including Supplementary Materials)

We numerically study the spin wave dynamics in an antidot lattice based on a Co/Pd multilayer structure with reduced perpendicular magnetic anisotropy at the edges of the antidots. This structure forms a magnonic crystal with a periodic antidot pattern and a periodic magnetization configuration consisting of out-of-plane magnetized bulk and in-plane magnetized rims. Our results show the different behavior of spin waves in the bulk and in the rims under varying out-of-plane external magnetic field strength, revealing complex spin-wave spectra and hybridizations between the modes of these two subsystems. A particularly strong magnon-magnon coupling, due to exchange interactions, is found between the fundamental bulk spin-wave mode and the second-order radial rim modes. However, the dynamical coupling between the spin-wave modes at low frequencies, involving the first-order radial rim modes, is masked by the changes in the static magnetization at the bulk-rim interface with magnetic field changes. The study expands the horizons of magnonic-crystal research by combining periodic structural patterning and non-collinear magnetization texture to achieve strong magnon-magnon coupling, highlighting the significant role of exchange interactions in the coupling., Comment: 10 pages, 5 figures + 6 pages, 10 figures

The generation of short spin-current pulses is essential for fast spintronic devices. So far, spin current pulses are generated by femtosecond laser pulses which drive spins from a ferromagnetic metal layer. However, the need for miniaturization, simplicity and energy efficiency favour electric-field control of spintronic devices over optic or thermal control. Here, we combine ab initio calculations of electronic density of states at MgO/Fe interface with continuous model for charge transport to investigate the dynamics of the spin-dependent potential. We demonstrate that the voltage-driven instability of the electronic band structure due to the electronic resonant states at the Fe/MgO interface results in the generation of the femtosecond spin-polarized current pulse with the spin polarization up to P=700% that propagates from the interface to the bulk. The dynamics of the current pulses driven by the Stoner instability depends neither on the dielectric relaxation time nor on the details of how the instability is achieved by changing the voltage, i.e. as long as the voltage changes are slow (quasi-static) with respect to the time determined by the spin diffusion constant, being of the order of fs.The presence of the instability may be detected by transport or magnetic measurements.

Confined spin-wave modes are a promising object for studying nonlinear effects and future quantum technologies. Here, using micromagnetic simulations, we use a microwave magnetic field from a coplanar waveguide (CPW) to pump a standing spin-wave confined in the cavity of magnonic crystal. We find that the frequency of the fundamental cavity mode is equal to the ferromagnetic resonance frequency of the plane film and overlaps with the magnonic bandgap, allowing high magnetic field tunability. Multi-frequency harmonics of the cavity mode are generated once the microwave amplitude surpasses a certain threshold. Specifically, the second and third harmonics at 0.5 T equate to 48.6 and 72.9 GHz with wavelengths of 44 and 22 nm respectively, which propagate into the crystal. This effect reaches saturation when the CPW covers the entire cavity, making the system feasible for realization. These processes show potential for the advancement of magnonics at high-frequencies and very short-wavelengths., Comment: 8 pages, 5 figures

The spin-wave dynamics in the thin CoFeB film in Damon-Eshbach geometry are studied in three cases of boundary conditions -- free boundary conditions, symmetrical surface anisotropy, and one-sided surface anisotropy. The analytical model created by Wolfram and De Wames was extended to include perpendicular surface anisotropy in boundary conditions. Its comparison with numerical simulations demonstrate perfect agreement between the approaches. The analysis of the dispersion relation indicates that the presence of surface anisotropy increases the avoided crossing size between Damon-Eshbach mode and perpendicular standing modes. Additionally, asymmetrical one-sided surface anisotropy induces nonreciprocity in the dispersion relation. In-depth analysis of the avoided crossing size is conducted for systems with different boundary conditions, different thicknesses, surface anisotropy constant values, and external magnetic fields. It shows the significant role of the strength of surface localization of Damon-Eshbach mode and the symmetry of perpendicular standing modes in the avoided crossing broadening. Interestingly, for specific set of parameters the interaction between the particular modes can be suppressed, resulting in a mode crossing. Such a crossing, which occurs only on one side of the dispersion relation in a one-sided surface anisotropy system, can be utilized in nonreciprocal devices., Comment: 15 pages, 9 figures

The research on the properties of spin waves (SWs) in three-dimensional nanosystems is an innovative idea in the field of magnonics. Mastering and understanding the nature of magnetization dynamics and binding of SWs at surfaces, edges, and in-volume parts of three-dimensional magnetic systems enables the discovery of new phenomena and suggests new possibilities for their use in magnonic and spintronic devices. In this work, we use numerical methods to study the effect of geometry and external magnetic field manipulations on the localization and dynamics of SWs in crescent-shaped (CS) waveguides. It is shown that changing the magnetic field direction in these waveguides breaks the symmetry and affects the localization of eigenmodes with respect to the static demagnetizing field. This in turn has a direct effect on their frequency. Furthermore, CS structures were found to be characterized by significant saturation at certain field orientations, resulting in a cylindrical magnetization distribution. Thus, we present chirality-based nonreciprocal dispersion relations for high-frequency SWs, which can be controlled by the field direction (shape symmetry) and its amplitude (saturation).

A new concept in magnonics studies the dynamics of spin waves (SWs) in three-dimensional nanosystems. It is a natural evolution from conventionally used planar systems to explore magnetization configurations and dynamics in 3D nanostructures with lengths near intrinsic magnetic scales. In this work, we perform broadband ferromagnetic resonance (BBFMR) measurements and micromagnetic simulations of nanoscale magnetic gyroids - a periodic chiral structure consisting entirely of chiral triple junctions. Our results show unique properties of the network, such as the localization of the SW modes, evoking their topological properties, and the substantial sensitivity to the direction of the static magnetic field. The presented results open a wide range of applications in the emerging field of 3D magnonic crystals and spintronics., Comment: This paper has been withdrawn due to a misunderstanding among the co-authors and lack of final approval for publication in its current form. The authors apologize for any confusion caused by its publication

We numerically demonstrate the excitation of leaky spin waves (SWs) guided along a ferromagnetic stripe by an obliquely incident SW beam on the thin film edge placed below the stripe. During propagation, leaky waves emit energy back to the layer in the form of plane waves and several laterally shifted parallel SW beams. This resonance excitation, combined with interference effects of the reflected and re-emitted waves, results in the magnonic Woods anomaly and significant increase of the Goos-Hanchen shift magnitude. Hence, we provide a unique platform to control SW reflection and to transfer SWs from a 2D platform into the 1D guiding mode that can be used to form a transdimensional magnonic router.

Controlling the vortex chirality in ferromagnetic nanodots and nanorings has been a topic of investigation for the last few years. Many control methods have been proposed and it has been found that the control is related to the breaking of the circular symmetry. In this paper, we present a theoretical study demonstrating the control of chirality in ferromagnetic nanoring without directly breaking its symmetry, but instead by placing elongated ferromagnetic nanoelement inside the ring, Here, the stray magnetostatic field exerted by the asymmetrically placed nanoelement determines the movement of the domain walls upon remagnetization of the nanoring and the resulting chirality in the remanence. This approach allows the chirality of the vortex state to be controlled and also promises its control in a dense array of nanorings, thus suitable for spintronic and magnonic applications., Comment: 7 pages, 5 figures

The magnetization dynamics in nanostructures has been extensively studied in the last decades, and nanomagnetism has evolved significantly over that time, discovering new effects, developing numerous applications, and identifying promising new directions. This includes magnonics, an emerging research field oriented on the study of spin-wave dynamics and their applications. In this context, thin ferromagnetic films with perpendicular magnetic anisotropy (PMA) offer interesting opportunities to study spin waves, in particular, due to out-of-plane magnetization in remanence or at relatively weak external magnetic fields. This is the only magnetization configuration offering isotropic in-plane spin-wave propagation within the sample plane, the forward volume magnetostatic spin-wave geometry. The isotropic dispersion relation is highly important in designing signal-processing devices, offering superior prospects for direct replicating various concepts from photonics into magnonics. Analogous to photonic or phononic crystals, which are the building blocks of optoelectronics and phononics, magnonic crystals are considered as key components in magnonics applications. Arrays of nanodots and structured ferromagnetic thin films with a periodic array of holes, popularly known as antidot lattices based on PMA multilayers have been recently studied. Novel magnonic properties related to propagating spin-wave modes, exploitation of the band gaps, and confined modes, were demonstrated. Also, the existence of nontrivial magnonic band topologies has been shown. Moreover, the combination of PMA and Dzyaloshinskii-Moriya interaction leads to the formation of chiral magnetization states, including N\'eel domain walls, skyrmions, and skyrmionium states.

We report on the evolution of the spin-wave spectrum under structural disorder introduced intentionally into one-dimensional magnonic quasicrystal. We study theoretically a system composed of ferromagnetic strips arranged in a Fibonacci sequence. We considered several stages of disorder in the form of phasonic defects, where different rearrangements of strips are introduced. By transition from the quasiperiodic order towards disorder, we show a gradual degradation of spin-waves fractal spectra and closing of the frequency gaps. In particular, the phasonic defects lead to the disappearance of the van Hove singularities at the frequency gap edges by moving modes into the frequency gaps and appearing new modes inside the frequency gaps. These modes disperse and eventually can close the gap, with increasing disorder levels. The work reveals how the the presence of disorder modifies the intrinsic spin wave localization existing in undefected magnonic quasicrystals. The paper contributes to the knowledge of magnonic Fibonacci quasicrystals and opens the way to study of the phasonic defects in two-dimensional magnonic quasicrystals.

Increasing amounts of information force the continuous improvement of information storage and processing technologies, further device miniaturization, and their efficiency increase. Magnetic skyrmions, topological quasiparticles, and the smallest stable magnetic textures possess intriguing properties and potential for data storage applications. Hybrid nanostructures with elements of different magnetization orientations can offer additional advantages for developing skyrmion-based spintronic and magnonic devices. We show that an N\'eel-type skyrmion confined within a nanodot placed on top of a ferromagnetic stripe produces a unique and compelling platform for exploring mutual coupling between magnetization textures. The skyrmion induces an imprint upon the stripe, which, in turn, asymmetrically squeezes the skyrmion in the dot, increasing their size and the range of skyrmion stability for small values of DMI, as well as introducing skyrmion bi-stability. At the end, we present a proof-of-concept technique for unconstrained transport of a skyrmion along a racetrack based on proposed hybrid systems. Our results demonstrate a hybrid structure that is promising for applications in magnonics and spintronics., Comment: 31 pages, 11 figures

Efficient numerical methods are required for the design of optimised devices. In magnonics, the primary computational tool is micromagnetic simulations, which solve the Landau-Lifshitz equation discretised in time and space. However, their computational cost is high, and the complexity of their output hinders insight into the physics of the simulated system, especially in the case of multimode propagating wave-based devices. We propose a finite-element modal method allowing an efficient solution of the scattering problem for dipole-exchange spin waves propagating perpendicularly to the magnetisation direction. The method gives direct access to the scattering matrix of the whole system and its components. We extend the formula for the power carried by a magnetostatic mode in the Damon-Eshbach configuration to the case with exchange, allowing the scattering coefficients to be normalised to represent the fraction of the input power transferred to each output channel. We apply the method to the analysis of spin-wave scattering on a basic functional block of magnonic circuits, consisting of a resonator dynamically coupled to a thin film. The results and the method are validated by comparison with micromagnetic simulations., Comment: Revised version

The phase is one of the fundamental properties of a wave that allows to control interference effects and can be used to efficiently encode information. We examine numerically a magnonic resonator of the Gires-Tournois interferometer type, which enables the control of the phase of spin waves reflected from the edges of the ferromagnetic film. The considered interferometer consists of a Py thin film and a thin, narrow Py stripe placed above its edge, both coupled magnetostatically. We show that the resonances and the phase of the reflected spin waves are sensitive for a variation of the geometrical parameters of this bi-layerd part of the system. The high sensitivity to film, stripe, and non-magnetic spacer thicknesses, offers a prospect for developing magnonic metasurfaces and sensors.

Magnonics is seen nowadays as a candidate technology for energy-efficient data processing in classical and quantum systems. Pronounced nonlinearity, anisotropy of dispersion relations and phase degree of freedom of spin waves require advanced methodology for probing spin waves at room as well as at mK temperatures. Yet, the use of the established optical techniques like Brillouin light scattering (BLS) or magneto optical Kerr effect (MOKE) at ultra-low temperatures is forbiddingly complicated. By contrast, microwave spectroscopy can be used at all temperatures but is usually lacking spatial and wavenumber resolution. Here, we develop a variable-gap propagating spin-wave spectroscopy (VG-PSWS) method for the deduction of the dispersion relation of spin waves in wide frequency and wavenumber range. The method is based on the phase-resolved analysis of the spin-wave transmission between two antennas with variable spacing, in conjunction with theoretical data treatment. We validate the method for the in-plane magnetized CoFeB and YIG thin films in $k\perp B$ and $k\parallel B$ geometries by deducing the full set of material and spin-wave parameters, including spin-wave dispersion, hybridization of the fundamental mode with the higher-order perpendicular standing spin-wave modes and surface spin pinning. The compatibility of microwaves with low temperatures makes this approach attractive for cryogenic magnonics at the nanoscale., Comment: 9 pages, 5 figures

The excitation of high-frequency short-wavelength spin waves is a challenge limiting the application of these propagating magnetization disturbances in information processing systems. We propose a method of local excitation of the high-frequency spin waves using the non-linear nature of magnetization dynamics. We demonstrate with numeric simulations that an edge-localized spin wave can be used to excite plane waves propagating obliquely from the film's edge at a doubled frequency and over twice shorter in wavelength. The excitation mechanism is a direct result of the ellipticity of the magnetic moments precession that is related to the edge-mode propagation. As a consequence, the magnetization component tangential to the equilibrium orientation oscillates with doubled temporal and spatial frequencies, which leads to efficient excitation of the plane spin waves. Threshold-less non-linear process of short-wavelength spin-wave excitation proposed in our study is promising for integration with an inductive or point-like spin-torque source of edge spin waves., Comment: This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Appl. Phys. Lett. 118, 062408 (2021) and may be found at https://doi.org/10.1063/5.0041030 or https://aip.scitation.org/doi/abs/10.1063/5.0041030

Spin waves are promising chargeless information carriers for the future, energetically efficient beyond-CMOS systems. Among many advantages there are the ease of achieving nonlinearity, the variety of possible interactions, and excitation types. Although the rapidly developing magnonic research has already yielded impressive realizations, multi-mode nonlinear effects, particularly with the propagating waves and their nanoscale realizations, are still an open research problem. We study theoretically the dynamic interactions of the spin waves confined to the edge of a thin ferromagnetic film with the spin-wave beam incident at this edge. We found the inelastically scattered spin-wave beams at frequencies increased and decreased by the frequency of the edge spin-wave relative to the specularly reflected beam. We observed a strong dependence of the angular shift of the inelastic scattered spin-wave beam on the edge-mode frequency, which allowed us to propose a magnonic demultiplexing of the signal encoded in spin waves propagating along the edge. Since dynamic magnetostatic interactions, which are ubiquitous in the spin-wave dynamics, are decisive in this process, this indicates the possibility of implementing the presented effects, also in other configurations and their use in magnonic systems.

The use of spin waves as a signal carrier requires developing the functional elements allowing for multiplexing and demultiplexing information coded at different wavelengths. For this purpose, we propose a system of thin ferromagnetic layers dynamically coupled by a rectangular ferromagnetic resonator. We show that a single and double, clockwise and counter-clockwise, circulating modes of the resonator offer a wide possibility of control of propagating waves. Particularly, at frequency related to the double-clockwise circulating spin-wave mode of the resonator, the spin wave excited in one layer is transferred to the second one where it propagates in the backward direction. Interestingly, the wave excited in the second layer propagates in the forward direction only in that layer. This demonstrates add-drop filtering, as well as circulator functionality. Thus, the proposed system can become an important part of future magnonic technology for signal routing., Comment: 6 pages, 4 figures

Using frequency-domain finite element calculations cross-checked with micromagnetic simulations, we demonstrate that the phase of spin waves reflected from an interface between a permalloy film and a bilayer can be controlled by changing dimensions of the bilayer. Treating the bilayer formed by the permalloy film and a ferromagnetic stripe as a segment of a multi-mode waveguide, we show that spin-wave Fabry-Perot resonances of one of its modes are responsible for the high sensitivity of the phase of reflected waves to stripe width and the stripe-film separation. Thus, the system is a unique realization of a fully magnonic Gires-Tournois interferometer based on a two-modes resonator, which can be treated as a magnonic counterpart of a metasurface, since it enables manipulation of the phase of spin waves at subwavelength distances. Knowledge gained from these calculations might be used to design magnonic devices such as flat lenses or magnetic particle detectors.

In magnonics, an emerging branch of wave physics characterized by low-energy consumption, it is highly desirable to realize circuit elements within the scope of spin-wave computing. Here, based on numerical simulations, we demonstrate the functionality of the spin-wave diode and the circulator to steer and manipulate spin waves over a wide range of frequency in the GHz regime. They take advantage of the unidirectional coupling induced by the interfacial Dzyaloshinskii-Moriya interaction to transfer the spin wave between thin ferromagnetic layers in only one direction of propagation. Using the multilayered structure consisting of Py and Co in direct contact with Pt, we obtain sub-micrometer-size devices of high efficiency. In the diode, the power loss ratio between forward and reverse direction reaches 22 dB, while in the four-port circulator, the efficiency exceeds 13 dB. Thus, our work contributes to the emerging branch of energy-efficient magnonic logic devices, where, thanks to short wavelength of spin waves, it is possible to realize nanoscale devices.

We present new mechanism for manipulation of the spin-wave amplitude through the use of the dynamic charge-mediated magnetoelectric effect in ultrathin multilayers composed of dielectric thin-film capacitors separated by a ferromagnetic bilayer. Propagating spin waves can be amplified and attenuated with rising and decreasing slopes of the oscillating voltage, respectively, locally applied to the sample. The way the spin accumulation is generated makes the interaction of the spin-transfer torque with the magnetization dynamics mode-selective and restricted to some range of spin-wave frequencies, which is in contrary to known types of the spin-transfer torque effects. The interfacial nature of spin-dependent screening allows to reduce the thickness of the fixed magnetization layer to a few nanometers, thus the proposed effect significantly contributes toward realization of the magnonic devices and also miniaturization of the spintronic devices.

The concept of Space-Time Crystals (STC), i.e. translational symmetry breaking in time and space, was recently proposed and experimentally demonstrated for quantum systems. Here, we transfer this concept to magnons and experimentally demonstrate a driven STC at room temperature. The STC is realized by strong homogeneous micro-wave pumping of a micron-sized permalloy (Py) stripe and is directly imaged by Scanning Transmission X-ray Microscopy (STXM). For a fundamental understanding of the formation of the STC, micromagnetic simulations are carefully adapted to model the experimental findings. Beyond the mere generation of a STC, we observe the formation of a magnonic band structure due to back folding of modes at the STC's Brillouin zone boundaries. We show interactions of magnons with the STC that appear as lattice scattering. This results in the generation of ultra short spin waves down to 100 nm wavelength that cannot be described by classical dispersion relations for linear spin wave excitations. We expect that room temperature STCs will be a useful tool to investigate non-linear wave physics, as they can be easily generated and manipulated to control their spatial and temporal band structure.

Spin waves are promising candidates for information carriers in advanced technology. The interactions between spin waves and acoustic waves in magnetic nanostructures are of much interest because of their potential application for spin wave generation, amplification and transduction. We investigate numerically the dynamics of magnetoelastic excitations in a one-dimensional magphonic crystal consisting of alternating layers of permalloy and cobalt. We use the plane wave method and the finite element method for frequency- and time-domain simulations, respectively. The studied structure is optimized for hybridization of specific spin-wave and acoustic dispersion branches in the entire Brillouin zone in a broad frequency range. We show that this type of periodic structure can be used for efficient generation of high-frequency spin waves.

The lateral shift of an optical beam undergoing a Brillouin light scattering on acoustic wave in the total internal reflection geometry is studied theoretically. It is shown that the lateral shift depends on polarization (longitudinal or transversal) of the acoustic wave, as well as on the type of the scattering process: direct one, when the scattered wave undergoes a lateral shift at reflection from the interface, and cascading one, when fundamental-frequency light beam is laterally shifted at reflection and then is scattered on the acoustic wave., Comment: 4 pages, 4 figures

We have examined the spin polarization of the electron current in a ferromagnetic metal induced by the spin-dependent surface screening at the dielectric-ferromagnetic metal (D-FM) interface. In an applied ac voltage, the dynamic band splitting driven by the changes in the screening charge at the D-FM interface develops spin accumulation. The resultant spin accumulation gradient produces a time-dependent spin current. We have derived the rate of the spin accumulation on the rate of the screening charge density accumulation within the Stoner band model. The spin-charge dynamics in the system is then modeled by a set of diffusive equations with the contributions from spin-dependent surface screening ands spin-dependent conductivity. We show for MgO-Cu-Co-MgO system that the spin-dependent screening in thin Co film produces spin accumulation 7 times higher than that obtained by the spin-dependent conductivity in thick Co films. We propose an experimental approach to validate our numerical predictions and to distinguish between spin accumulation induced by the spin-dependent conductivity and by the spin-dependent surface screening.

By combining Brillouin Light Scattering and micromagnetic simulations we studied the spin-wave dynamics of a Co/Pd thin film multilayer, features a stripe domain structure at remanence. The periodic up and down domains are separated by cork-screw type domain walls. The existence of these domains causes a scattering of the otherwise bulk and surface spin-wave modes, which form mode families, similar to a one dimensional magnonic crystal. The dispersion relation and mode profiles of spin waves are measured for transferred wave vector parallel and perpendicular to the domain axis., Comment: 18 pages, 3 figures

We present a theoretical investigation of the polarization plane rotation at light transmission - Faraday effect, through one-dimensional multilayered magneto-photonic systems consisting of periodically distributed magnetic and dielectric layers. We calculate Faraday rotation spectra of photonic-magnonic crystals, where cell (or supercell) is composed of magnetic layer and dielectric layer (or section of dielectric photonic crystal). We found that the Faraday rotation of p-polarized incident light is increasing in the transmission band with the number of magnetic supercells. The increase of Faraday rotation is observed also in vicinity of the band-gap modes localized in magnetic layers but the maximal polarization plane rotation angles are reached at minimal transmittivity. We show that presence of linear magneto-electric interaction in the magnetic layers leads to significant increase of the Faraday rotation angles of s-polarized incident light in the vicinity of the fine-structured modes inside the photonic-band-gap., Comment: 7 pages

Magnonic quasicrystals exceed the possibilities of spin wave (SW) manipulation offered by regular magnonic crystals, because of their more complex SW spectra with fractal characteristics. Here, we report the direct x-ray microscopic observation of propagating SWs in a magnonic quasicrystal, consisting of dipolarly coupled permalloy nanowires arranged in a one-dimensional Fibonacci sequence. SWs from the first and second band as well as evanescent waves from the band gap between them are imaged. Moreover, additional mini-band gaps in the spectrum are demonstrated, directly indicating an influence of the quasiperiodicity of the system. The experimental results are interpreted using numerical calculations and we deduce a simple model to estimate the frequency position of the magnonic gaps in quasiperiodic structures. The demonstrated features of SW spectra in one-dimensional magnonic quasicrystals allows utilizing this class of metamaterials for magnonics and makes them an ideal basis for future applications., Comment: 10 pages, 6 figures

We investigate magnonic band structure in thin homogeneous permalloy film decorated with periodic array of elliptically shaped permalloy dots and separated by non-magnetic Pt spacer. We demonstrated experimentally formation of the magnonic band structure for Damon-Eshbach wave propagating in permalloy film with the band gap opened at the Brillouin zone border and band splitting at smaller wavenumbers, due to the Bragg interference and interaction of propagating wave of the continuous film with a standing resonant mode of the nano-ellipses, respectively. The shape anisotropy of the permalloy nanodots allows to control the spin wave dynamics through the switch between two states of the magnetization with respect to the underneath film magnetization, thus enabling magnonic band structure reprogrammability. With numerical analysis we show, that predominant role in formation of the magnonic band structure is played by a vertical dynamic coupling between propagating wave in the film and magnetization oscillations in the nanodots., Comment: 7 pages, 8 figures

The possibility to generate short spin waves is of great interest in the field of magnonics nowadays. We present an effective and technically affordable way of conversion of long spin waves, which may be generated by conventional microwave antenna, to the short, sub-micrometer waves. It is achieved by grating-assisted resonant dynamic dipolar interaction between two ferromagnetic layers separated by some distance. We analyze criteria for the optimal conversion giving a semi-analytical approach for the coupling coefficient. We show by the numerical calculations the efficient energy transfer between layers which may be either of co-directional or contra-directional type. Such a system may operate either as a short spin wave generator or a frequency filter, moving foreward possible application of magnonics.

Using analysis of iso-frequency contours of the spin-wave dispersion relation, supported by micromagnetic simulations, we study the propagation of spin-wave (SW) beams in thin ferromagnetic films through the areas of the inhomogeneous refractive index. We compare the transmission and reflection of SWs in areas with gradual and step variation of the SW refractive index. In particular, we show the mirage effect for SWs with narrowing SW beam width, and an application of the gradual modulation of the SWs refractive index as a diverging lens. Furthermore, we study the propagation of SWs in ferromagnetic stripe with modulated refractive index. We demonstrate that the system can be considered as the graded-index waveguide, which preserves the width of the SW beam for a long distance-the property essential for prospective applications of magnonics.

We have investigated co-directional and contra-directional couplings between spin wave and acoustic wave in one-dimensional periodic structure (magphonic crystal). The system consists of two ferromagnetic layers alternating in space. We have taken into consideration materials commonly used in magnonics: yttrium iron garnet, CoFeB, permalloy, and cobalt. The coupled mode theory (CMT) formalism have been successfully implemented to describe magnetoelastic interaction as a periodic perturbation in the magphonic crystal. The results of CMT calculations have been verified by more rigorous simulations by frequency-domain plane wave method and time-domain finite element method. The presented resonant coupling in the magphonic crystal is an active in-space mechanism which spatially transfers energy between propagating spin and acoustic modes, thus creating propagating magnetoelastic wave. We have shown, that CMT analysis of the magnetoelastic coupling is an useful tool to optimize and design a spin wave - acoustic wave transducer based on a magphonic crystals. The effect of spin wave damping has been included to the model to discuss the efficiency of such a device. Our model shows that it is possible to obtain forward conversion of the acoustic wave to the spin wave in case of co-directional coupling and backward conversion in case of contra-directional coupling.

We studied the effect of collimation for monochromatic beams of spin waves, resulting from the refraction at the interface separating two magnetic half-planes. The collimation was observed in broad range of the angles of ncidence for homogenous Co and Py half-planes, due to significant intrinsic anisotropy of spin wave propagation in these materials. The effect exists for the sample saturated by in plane magnetic field tangential to the interface. The collimation for all possible angles of incidence was found in the system where the incident spin wave is refracted on the interface between homogeneous and periodically patterned layers of YIG. The refraction was investigated by the analysis of isofrequency dispersion contours of both pairs materials, i.e., uniform YIG/patterned YIG and Co/Py, which are calculated with the aid of the plane wave method. Besides, the refraction in Co/Py system was studied using micromagnetic simulations.

Color filters have important applications in the area of Nano-spectroscopy and ccd imaging applications. Metallic nanostructures provide an efficient way to design and engineer ultrathin color filters. These nanostructures have capability to split the white light into fundamental colors and enable color filters with ultrahigh resolution but their efficiency can be restricted due to high losses in metals especially at the visible wavelengths. In this work, we demonstrate Si nanoantennas based all-dielectric color filters, which are sensitive to incident-wave polarization and, thus, tunable with the aid of polarization angle variation. Two different information can be encoded in two different polarization states in a single physical nanostructure. The nanoantenna based pixels are highly efficient and can provide high quality of colors due to low losses in dielectric at optical frequencies. We experimentally demonstrate that a variety of colors can be achieved by changing the physical size of the nonsymmetric cross-shaped nanoantennas. The proposed devices cover an extended gamut of colors on CIE-1931 chromaticity diagram due to the existence of high quality resonance in Si nanoantennas. The device shows significant tunability of color while operating this color filter device in transmission as well as in reflection mode.